A power cable of copper is stretched straight between two fixed towers. If the temperature decreases, the cable tends to contract . The amount of contraction for a free copper cable or rod is 0.0017% per degree centigrade. Estimate what temperature decrease will cause the cable to snap. Pretend that the cable obeys young moduli until it reaches its breaking point. Ignore the weight of the cable and the sag and stress produced by the weight.
I was trying: $$\frac{\Delta L}{L} = \frac{F}{AY}$$
the ultimate strenght of copper and youg modulus are:
$$ U_s = 2.4\times10^8 $$ $$Y = 11\times10^{10}$$
I also notice: $$\Delta L \propto C°$$ then:
$$C° = \frac{U_s}{Y}L$$
however I dont have L does anyone have an idea?
Given the equation $\frac{\Delta L}{L} = \frac{U_s}{Y}$, we then have that at the point when the cable breaks, $\frac{\Delta L}{L} \approx \frac{2.4 \times 10^8}{11 \times 10^{10}} \approx 0.00218 = 0.218\%$.
So given the contraction is $0.0017\%$ per degree centigrade, i.e. $\frac{\Delta L}{L} = 0.000017 * \Delta T$ (where $T$ is temperature), then we get that $\Delta T = \frac{0.00218}{0.000017} \approx 128$. So the temperature would need to decrease by about 128 degrees Celsius (quite a large amount) in order for the cable to snap. Hopefully I'm understanding this problem correctly; I haven't worked with these ideas in physics in quite a while.